Integrals 101 to 200

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(2-m)/(2*b*d*x+a*d+b*c)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1787\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (c+d x)^{2-m}}{(b c+a d+2 b d x)^4} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(2-m)/(2*b*d*x+a*d+b*c)**4,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1788\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x)^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1796\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1797\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1798\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (c+d x)^n}{e+f x} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n/(f*x+e),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1799\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^{3+n} (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**(3+n)*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1810\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^{2+n} (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**(2+n)*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1811\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^{1+n} (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**(1+n)*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1812\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^n (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**n*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1813\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^{-1+n} (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**(-1+n)*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1814\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^{-2+n} (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**(-2+n)*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1815\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^n (e+f x)^{-3+n} (a (d e+c f)+2 a d f x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(f*x+e)**(-3+n)*(a*(c*f+d*e)+2*a*d*f*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/22_1.1.1.3d

Test file number \(22\)

Integral number in file \(1816\)

Sympy [F(-2)]

Exception generated. \[ \int x (a+b x)^m (c+d x)^n (e+f x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x*(b*x+a)**m*(d*x+c)**n*(f*x+e),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/23_1.1.1.4a

Test file number \(23\)

Integral number in file \(229\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/23_1.1.1.4a

Test file number \(23\)

Integral number in file \(230\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (c+d x)^n (g+h x)}{\sqrt {e+f x}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(h*x+g)/(f*x+e)**(1/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/23_1.1.1.4a

Test file number \(23\)

Integral number in file \(231\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (c+d x)^3}{(e+f x) (g+h x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**3/(f*x+e)/(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(117\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (c+d x)^2}{(e+f x) (g+h x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**2/(f*x+e)/(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(118\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m}{(c+d x) (e+f x) (g+h x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m/(d*x+c)/(f*x+e)/(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(121\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^4 (e+f x)^n}{(a+b x) (c+d x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**4*(f*x+e)**n/(b*x+a)/(d*x+c),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(123\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m}{(c+d x) (e+f x) (g+h x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m/(d*x+c)/(f*x+e)/(h*x+g),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(133\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(134\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(135\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x)^2 (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e)**2*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(139\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n (e+f x)^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(140\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{1-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(1-m)*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(144\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(f*x+e)*(h*x+g)/((d*x+c)**m),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(145\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-1-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(-1-m)*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(146\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-2-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(-2-m)*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(147\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-3-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(-3-m)*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(148\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-4-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**(-4-m)*(f*x+e)*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(149\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^2 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**2*(d*x+c)**(-4-m)*(f*x+e)**m*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(150\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x) (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(d*x+c)**(-4-m)*(f*x+e)**m*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(151\)

Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**(-4-m)*(f*x+e)**m*(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(152\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^m (e+f x)^n}{(a+b x) (c+d x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**m*(f*x+e)**n/(b*x+a)/(d*x+c),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(153\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x)^m (A+B x) (c+d x)^{-m}}{e+f x} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(B*x+A)/((d*x+c)**m)/(f*x+e),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/24_1.1.1.4b

Test file number \(24\)

Integral number in file \(154\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(179\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^{3/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**(3/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(185\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^{5/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(186\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^{9/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**(9/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(188\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^{11/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**(11/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(189\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (A+B x) (c+d x)^n \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(B*x+A)*(d*x+c)**n,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(190\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n \left (A+B x+C x^2\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(C*x**2+B*x+A),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(191\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^n \left (A+B x+C x^2+D x^3\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**m*(d*x+c)**n*(D*x**3+C*x**2+B*x+A),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.1_Linear_binomial/26_1.1.1.6

Test file number \(26\)

Integral number in file \(192\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b \sqrt {x}\right )^p x^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**(1/2))**p*x**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.2/47_1.1.3.2_e

Test file number \(47\)

Integral number in file \(154\)

Sympy [F(-2)]

Exception generated. \[ \int (d x)^m \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((d*x)**m*(c*(b*x**2+a)**3)**(3/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.2/49_1.1.3.2_g

Test file number \(49\)

Integral number in file \(60\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+b x^n\right ) \left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(86\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+b x^n\right ) \left (c+d x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)/(c+d*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(87\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(92\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+b x^n\right )^2 \left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)**2/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(93\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(123\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(124\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b x^n\right )^p \left (c+d x^n\right )^{-1-\frac {1}{n}-p} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**n)**p*(c+d*x**n)**(-1-1/n-p),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(126\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{-1/n}}{a+b x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)/((c+d*x**n)**(1/n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(131\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{1-\frac {1}{n}}}{\left (a+b x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((c+d*x**n)**(1-1/n)/(a+b*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(132\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{2-\frac {1}{n}}}{\left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((c+d*x**n)**(2-1/n)/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(133\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b x^n\right )^p \left (c+d x^n\right )^{-2-\frac {1}{n}-p} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**n)**p*(c+d*x**n)**(-2-1/n-p),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(134\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{-1-\frac {1}{n}}}{a+b x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((c+d*x**n)**(-1-1/n)/(a+b*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(139\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{-1/n}}{\left (a+b x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)**2/((c+d*x**n)**(1/n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(140\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{1-\frac {1}{n}}}{\left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((c+d*x**n)**(1-1/n)/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(141\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^n\right )^{2-\frac {1}{n}}}{\left (a+b x^n\right )^4} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((c+d*x**n)**(2-1/n)/(a+b*x**n)**4,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(142\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b x^n\right )^p \left (c+d x^n\right )^q \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**n)**p*(c+d*x**n)**q,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/52_1.1.3.3_c

Test file number \(52\)

Integral number in file \(143\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (c+d x^{2 n}\right )^p}{\left (a-b x^n\right ) \left (a+b x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((c+d*x**(2*n))**p/(a-b*x**n)/(a+b*x**n),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.3/53_1.1.3.3_d

Test file number \(53\)

Integral number in file \(5\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b \sqrt {x}\right )^p \left (c+d \sqrt {x}\right )^q x^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**(1/2))**p*(c+d*x**(1/2))**q*x**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(252\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b \sqrt {x}\right )^p \left (c+d \sqrt {x}\right )^q (e x)^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**(1/2))**p*(c+d*x**(1/2))**q*(e*x)**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(253\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^n}{x^3 \left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*x**n)/x**3/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(287\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^n}{x^4 \left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*x**n)/x**4/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(288\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^n}{x^{7/2} \left (a+b x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*x**n)/x**(7/2)/(a+b*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(323\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{3/2} \left (A+B x^n\right )}{\left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(3/2)*(A+B*x**n)/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(324\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^n}{\sqrt {x} \left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*x**n)/x**(1/2)/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(326\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^n}{x^{3/2} \left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*x**n)/x**(3/2)/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(327\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^n}{x^{5/2} \left (a+b x^n\right )^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*x**n)/x**(5/2)/(a+b*x**n)**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(328\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{x^3 \left (a+b x^n\right ) \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/x**3/(a+b*x**n)/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(441\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^2}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**2/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(442\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(443\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(444\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{x \left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/x/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(445\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{x^2 \left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/x**2/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(446\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{x^3 \left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/x**3/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(447\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+2 n}}{\left (a+b x^n\right ) \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1+2*n)/(a+b*x**n)/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(455\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+2 n}}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1+2*n)/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(456\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+2 n}}{\left (a+b x^n\right )^3 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1+2*n)/(a+b*x**n)**3/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(457\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+3 n}}{\left (a+b x^n\right ) \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1+3*n)/(a+b*x**n)/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(461\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+3 n}}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1+3*n)/(a+b*x**n)**2/(c+d*x**n),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(462\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+3 n}}{\left (a+b x^n\right )^3 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1+3*n)/(a+b*x**n)**3/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(463\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(e x)^m}{\left (a+b x^n\right )^2 \left (c+d x^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((e*x)**m/(a+b*x**n)**2/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(492\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (-1+p)} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(-1+p))*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(495\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(e x)^m \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((e*x)**m*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(500\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(e x)^m \left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((e*x)**m*(a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(501\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (3+p)} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(3+p))*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(517\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (3+p)} \left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(3+p))*(a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(518\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (2+p)} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(2+p))*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(523\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (2+p)} \left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(2+p))*(a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(524\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (1+p)} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(p+1))*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(529\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (1+p)} \left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(p+1))*(a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(530\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n p} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-n*p-1)*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(536\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n p} \left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-n*p-1)*(a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(537\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (-1+p)} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(-1+p))*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(542\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (-1+p)} \left (a+b x^n\right )^p}{\left (c+d x^n\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(-1+p))*(a+b*x**n)**p/(c+d*x**n)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(543\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-n (-2+p)} \left (a+b x^n\right )^p}{c+d x^n} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**(-1-n*(-2+p))*(a+b*x**n)**p/(c+d*x**n),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test file number \(56\)

Integral number in file \(549\)